The speed of the river current with respect to the boat is(Vₙ)= 1.036 m/s.
Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
To calculate the values of the speed of the river, we are using the formula,
v=1.768-Vₙ
The given parameters;
speed of boat, vₐ= 2.5 m/s
width of the river, w = 285 m
distance upstream, d = 118 m
direction of the pilot, θ = 45⁰
The vertical and horizontal component of the velocity is calculated as follows;
v(x)=vₐsinθ=2.5*sin45°=1.768m/s
v(y)=vₐcosθ=2.5*cos45°=1.768m/s
The time taken for the boat to cross the river is calculated as follows;
t=w/v(y)
Or, t=285/1.768
Or, t = 161.25 s
The total horizontal velocity of the boat and the river is calculated as;
v=1.768-Vₙ
Or,1.768-Vₙ=d/t
Or, 1.768-Vₙ=118/161.2
Or, 1.768-Vₙ=0.732
Or, Vₙ=1.036m/s
From the above calculation we can conclude that,
The speed of the river current with respect to the boat is 1.036 m/s.
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Question: A boat, whose speed in still water is 2.50 m/s, must cross a 285-m wide river and arrive at a point 118m upstream from where it starts. To do so, the pilot must head the boat at a 45.0 degrees upstream angle. What is the speed of the rivers current?
